As one flow meter there is an ultrasonic flow meter that uses the difference in propagation times produced when an ultrasonic wave propagates within a medium. As illustrated in FIG. 10, for example, the ultrasonic flow meter has ultrasonic transceivers 10 and 11 disposed in a flow path, and measures the speed of flow of a medium, such as a gas or a liquid, that flows in the flow path, based on the difference in propagation times between the propagation time of a received signal 12 that is received on the downstream side when an ultrasonic wave is transmitted from the upstream side, and the propagation time of a received signal 13 that is received on the upstream side when an ultrasonic wave is transmitted from the downstream side.
In the measurement of the difference in the propagation times, it is necessary to have a resolution in the order of nanoseconds or sub-nanoseconds. On the other hand, the ultrasonic waves used in ultrasonic flow meters have frequencies in the order of tens of kilohertz through 1 MHz, and thus the period of the signals is in excess of 1 μs, and thus the measured propagation times are susceptible to the influence of noise. However, the amplitude of the ultrasonic waves is affected by the speed of flow and state of flow of the medium within the flow path. Consequently, when the arrival of the ultrasonic wave is evaluated through setting a threshold value for the received signal, the arrival time that is measured will vary depending on the change in the amplitude of the received signal. That is, as illustrated in FIG. 11, in contrast to the time of arrival of the received signal S1, having a normal amplitude, at the threshold value TH1 being T1, the time of arrival of the received signal S2, having a smaller amplitude, at the threshold value TH1 will be T2.
Given this, there is a correlation method as a method for measuring that is not influenced by the change in the amplitude of the received signal. In the correlation method, the correlation between the received signal 12 that is transmitted from the ultrasonic transceiver 10 on the upstream side and received by the ultrasonic transceiver 11 on the downstream side and the received signal 13 that is transmitted by the ultrasonic transceiver 11 on the downstream side and received by the ultrasonic transceiver 10 on the upstream side is calculated, to calculate the difference in the propagation time from the position of the peak (the position of the maximum) of the correlation. This correlation is calculated through digital signal processing, and thus is caused to be discreet, with intervals that are the same as the sampling period of the received signals. While, as described above, the measurement of the difference in the propagation times requires an accuracy in the order of nanoseconds or sub-nanoseconds, the sampling frequency is, at most, in the order of tens of megahertz (where the sampling period is in the order of tens of nanoseconds), and thus it is necessary to perform interpolation of the discrete signals in order to measure the difference in propagation times with adequate accuracy.
If the transmitted signal of the ultrasonic wave is a burst wave comprising a signal of several periods wherein the frequency and the amplitude are held constant, then, as illustrated in FIG. 12, the received signal will have a waveform that has periodicity and wherein the amplitude changes. Consequently, the correlation function between the aforementioned two signals will have a strong component at the frequency of the burst wave. Because of this, the correlation function will have a form near to that of a trigonometric function, where the position of the peak can be interpolated using a quadratic function as an approximation. However, even when interpolating using a quadratic function, still there will be error between the value calculated using interpolation and the value that should actually be calculated. For example, let us assume that a correlation such as illustrated in FIG. 13 has been obtained for a sampling period of 20 ns. FIG. 14 shows an enlargement of the waveform in the vicinity of A in FIG. 13, which is the position of the peak of the correlation. FIG. 14 illustrates the discrete correlation functions indicated by the plot, and the curve, indicated by the dotted line, obtained through interpolation of the discrete correlation functions using quadratic functions. Note that in FIG. 13 and FIG. 14 the correlations were calculated using the signals received by producing to receive signals with a 15 ns time difference therebetween, and, from FIG. 14, it can be seen that there is a correlation peak in the vicinity of 15 ns. FIG. 15 shows, on the horizontal axis, the time difference between the two received signals, showing the position of the peak, derived from the interpolated correlation characteristics, and the error from the actual time difference, where it can be understood that, at the maximum, an error of more than 400 ps (0.4 nanoseconds) is produced. As mentioned previously, it is necessary to have a resolution in the order of nanoseconds or sub-nanoseconds in the difference between propagation times, so an error of 400 ps will negatively affect the measurement results. On the other hand, if a higher-order correlation were used for the interpolation, the interpolation formula would become complex, and would not be practical.
Given this, there is a method of calculating the position of the peak of the correlations using a Hilbert transform. (See, Japanese Unexamined Patent Application Publication 2002-243514 (“JP '514”)). This method enables the calculation of the peak position through a linear approximation, enabling the error to be reduced relative to interpolation using a quadratic function.
In the conventional technology disclosed in JP '514, the structure is one wherein a Hilbert transform is performed after calculating the correlations, and the position of the peak of the correlations is detected based on the positional relationships, to thereby derive the time difference. Specifically, the structure comprises A/D converters 200 and 210, correlation calculating means 220, a Hilbert transform portion 230, a phase relationship deriving portion 240, and maximal value detecting means 250, as illustrated in FIG. 16. However, this structure has a problem in that the computational overhead is too great.
Given this, in one form of embodiment according to the present invention, one object is to provide a calculating device that can reduce the computational overhead, even when calculating the difference in the propagation times with high accuracy, through the use of the Hilbert transform.